The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

Numeracy is one of the essential competencies that the objectives of teaching math to primary students should be towards. However, many research findings show that the problem of "innumeracy" frequently exists at primary schools. That means children still do not feel at home in the world of numbers and operations. Therefore, the paper…

This article illustrates and differentiates the unique role cognitive interviews and think-aloud interviews play in developing and validating assessments. Specifically, we describe the use of (a) cognitive interviews to gather empirical evidence to support claims about the intended construct being measured and (b) think-aloud interviews to gather…

Measurement and statistical investigation are areas of mathematics visibly neglected in educational intervention research, particularly studies involving students with or at risk for mathematics difficulties (MD). This shortage is concerning given the importance these areas hold in students' pursuit of mathematical proficiency. This study…

Measurement and statistical investigation are areas of mathematics visibly neglected in educational intervention research, particularly studies involving students with or at risk for mathematics difficulties (MD). This shortage is concerning given the importance these areas hold in students' pursuit of mathematical proficiency. This study…

Spatial skills have been consistently linked to mathematics achievement in older students and adults, but we know little about their relationship to mathematics achievement in elementary school. This study examined how spatial skills influenced the development of number sense, and subsequent mathematics competency, as students progressed from the…

One crucial issue in mathematics development is how children come to spontaneously apply arithmetical principles (e.g. commutativity). According to expertise research, well-integrated conceptual and procedural knowledge is required. Here, we report a method composed of two independent tasks that assessed in an unobtrusive manner the spontaneous…

The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early…

The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early…

The purpose of this study was to compare subgroups of students with various forms of learning difficulties (< 25th percentile) on cognitive and mathematics characteristics. Students with mathematics difficulty (MD, n = 105), reading difficulty (RD, n = 65), both (MDRD, n = 87), or neither (NoLD, n = 403) were evaluated on an array of cognitive…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

The purpose of the study was to examine differences in early numerical competencies, as well as subtraction skill, as a function of children's mathematics difficulty (MD) status: computational difficulty (CD), word problem-solving difficulty (PD), concurrent difficulty (CDPD), or neither difficulty (i.e., typically developing; TYP). Based on…

Response to intervention (RTI) is a framework in which interventions are implemented mostly in general education classes to resolve academic difficulties and help to mitigate contextual variables (i.e., lack of instruction, socio economic status, cultural differences, etc.) as an explanation for academic failure. The implementation of…

The purpose of the research is to explore second graders' concept of number development and quantitative reasoning. For this purpose, there were two stages of trials for the children. The first trial was concrete objects. After three months, the children participated in the second trial of half concrete objects. Since understanding the process of…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…